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\begin{figure}\begin{center}\BoxedEPSF{Polyiamonds.epsf scaled 1200}\end{center}\end{figure}

A generalization of the Polyominoes using a collection of equal-sized Equilateral Triangles (instead of Squares) arranged with coincident sides. Polyiamonds are sometimes simply known as Iamonds.

The number of two-sided (i.e., can be picked up and flipped, so Mirror Image pieces are considered identical) polyiamonds made up of $n$ triangles are 1, 1, 1, 3, 4, 12, 24, 66, 160, 448, ... (Sloane's A000577). The number of one-sided polyiamonds composed of $n$ triangles are 1, 1, 1, 4, 6, 19, 43, 121, ... (Sloane's A006534). No Holes are possible with fewer than seven triangles.

The top row of 6-polyiamonds in the above figure are known as the Bar, Crook, Crown, Sphinx, Snake, and Yacht. The bottom row of 6-polyiamonds are known as the Chevron, Signpost, Lobster, Hook, Hexagon, and Butterfly.

See also Polyabolo, Polyhex, Polyomino


Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

Gardner, M. ``Mathematical Games.'' Sci. Amer., Dec. 1964.

Golomb, S. W. Polyominoes: Puzzles, Patterns, Problems, and Packings, 2nd ed. Princeton, NJ: Princeton University Press, pp. 90-92, 1994.

Sloane, N. J. A. Sequences A000577/M2374 and A006534/M3287 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 342-343, 1993.

© 1996-9 Eric W. Weisstein